Question

A basketball player has a 50% chance of making each free throw. what is the probability that the player makes exactly five out of eleven free throws?

Answer 1

Free throw follows binomial distribution.
probability of making free throw = probability of success = 0.5 = p
probability of fail = 1-0.5 = 0.5 = q

Binomial distribution is given by,
P(X) = $^nC_{x} p^{x} q^{n-x}$

where n=11, x=5
Therefore,
P(X=5) =  $^(11)C_{5} (0.5)^{5} (0.5)^{11-5}$ = 0.2255